Saving power by managing the state of inactive computing devices

ABSTRACT

A system method and computer program product for managing readiness states of a plurality of computing devices. In response to a request, a computer system operates to either: provide one or more computing devices from an inactive pool to an active pool, or accept one or more active computing devices into the inactive pool. An Inactive Pool Manager proactively manages the inactive states of each computing device by: determining the desired number (and identities) of computing devices to be placed in each inactive state of readiness by solving a constraint optimization problem that describes a user-specified trade-off between expected readiness (estimated time to be able to activate computing devices when they are needed next) and conserving energy; generating a plan for changing the current set of inactive states to the desired set; and, executing the plan. Multiple alternative ways of quantifying the desired responsiveness to surges in demand are provided.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present invention claims priority to commonly-owned, co-pending U.S.patent application Ser. No. 12/939,635 filed Nov. 4, 2010, the entirecontents and disclosure of which is incorporated by reference as iffully set forth herein.

FIELD OF INVENTION

The present invention relates generally to power management techniquesfor computing systems, such as server farms or clusters in data centers,for instance.

BACKGROUND

The cost of data center server power consumption and the cooling systemsto dissipate the generated heat are major expenses in modern datacenters where thousands of servers are densely packed in relativelysmall racks. To maintain effective operation and sustain profitability,it becomes necessary to have power management systems to optimize thepower usage with respect to customer requirements. In other words, thesepower management systems must be able to use minimum power possible andyet be able to satisfy all customer requirements. It is well establishedthat a typical server consumes a relatively high amount of power even itis idle, due to chip leakage current and other supporting componentssuch as disk drives and network routers. Turning a system off anddirecting all traffic to a subset of available servers during non-peakhours is a common approach to saving power during periods of lowtraffic. Current technologies for server shutdown are mainly based onmanual actions by system administrators or on automated actions drivenby simple policies. Based on their experiences and workload history, thesystem operators may shut down systems for an extended period of time.In doing so, these system operators must anticipate the possibility ofsudden increases in traffic, and often they drastically overprovision toensure adequate performance (and hence customer satisfaction) even underworst case situations. The amount of manual effort by systemadministrators is costly, and so is the over provisioning that istypically done to ensure that performance goals are met—particularly asenergy costs continue to mount.

New power management strategies that turn servers on and off in realtime as workload fluctuates have been investigated. While turning aserver off can save energy costs, and perhaps licensing fees as well, acountervailing factor that must be considered is the cost of turning aserver on or off. There are several components to this cost. First,during the time that a server is being powered down or up, it is stillconsuming energy but is not doing any useful work. Second, every time aserver is power-cycled, the thermal changes induce more wear and tear onthe server, and thus frequent cycling may shorten the lifetime of theserver, leading to an increased failure rate and a concomitant increasein replacement cost. Third, 1 to 5 minutes may elapse when restoring aserver from shut-down state to a state in which it is fully availablefor use, depending on system applications and configurations. This maynot be fast enough to react to a sudden increase in traffic, resultingin Service Level Agreements (SLA) violations, which may be subject tomonetary penalties. All of these problematic costs reduce the usefulnessof the strategy of turning servers on and off dynamically, preventingpower management strategies of this nature from being deployed widely.

It is therefore desirable to place these unneeded devices intointermediate states of “readiness” such as “standby” or “hibernate” fromwhich the devices may be activated more quickly. These states consumemore power than when the device is powered down, and generally havelonger activation times than the idle state. Moreover, as common in datacenter environments with distributed resources, the overallinfrastructure is generally composed of different physical componentswith different power-performance characteristics, different powermanagement capabilities and different power-state-transition latencies.Therefore, the overall system efficiency can vary dramatically by theorder which the hosts are chosen to transition into different powerstates.

At present, there are no algorithms known in the art for managing thesetradeoffs between the desire to conserve energy and the desire to beresponsive to surges in workload behavior.

SUMMARY

The present invention is a system, method and computer program productthat addresses the tradeoff between responsiveness and power savings bycoordinating multiple surge response zones in a computing cluster withdifferent power-management states system characteristics.

In one embodiment, the tradeoffs between responsiveness and powersavings are formulated as an objective function with constraints, andthe desired number of devices in each inactive state emerging as thesolution to a constraint optimization problem.

Thus, in one aspect, there is provided a system, method and computerprogram product for managing power consumption in a system comprisingcomputing devices. The method comprises: receiving, at a processingunit, a request to one of: activate or deactivate one or more computingdevices from a respective group of inactive or active computing devices,each inactive or active computing device initially in a pre-determinedstate of readiness; activating or deactivating the one or more computingdevices, the activating or deactivating resulting in a number ofcomputing devices in one or more states of readiness i; optimizingconfiguration of the computing devices in the one or more states ofreadiness i by minimizing an expected power consumption Σ_(i) A_(i)P_(i) where i represents all inactive computing devices, A_(i)represents a number of the computing devices currently in each state i,and, P_(i) represents an average power consumption of a computingdevices while in the state i; and placing the computing devices in theoptimized configuration. A program using the processor unit isconfigured to perform one or more of the receiving, activating,optimizing and placing.

Further to this aspect, there are defined multiple alternative ways ofquantifying the desired responsiveness to surges in demand and, in eachcase, formulating tradeoffs between responsiveness and power savings asan objective function with constraints, and the desired number ofdevices in each inactive state emerges as the solution to a constraintoptimization problem.

Thus, the method further comprises: formulating, for processing by saidprocessor unit, a constraint optimization problem including an objectivefunction with constraints representing respective tradeoffs betweentransition time responsiveness and power savings; and, solving saidconstraint optimization problem to determine a number of devices to beplaced in each inactive state of readiness.

In a further aspect, there is provided a system for managing inactivestates of computing devices comprising: receiving, at a processing unit,a request to one of: activate or deactivate one or more computingdevices from a respective group of inactive or active computing devices,each inactive or active computing device initially in a pre-determinedstate of readiness; activating or deactivating the one or more computingdevices, the activating or deactivating resulting in a number ofcomputing devices in one or more states of readiness i; optimizingconfiguration of the computing devices in the one or more states ofreadiness i by minimizing an expected power consumption Σ_(i) A_(i)P_(i) where i represents all inactive computing devices, A_(i)represents a number of the computing devices currently in each state i,and, P_(i) represents an average power consumption of a computingdevices while in the state i; and placing the computing devices in theoptimized configuration. A program using the processor unit isconfigured to perform one or more of the receiving, activating,optimizing and placing.

A computer program product is provided for performing operations. Thecomputer program product includes a storage medium readable by aprocessing circuit and storing instructions run by the processingcircuit for running a method. The method is the same as listed above.

Further, in accordance with one embodiment, provision is made forpermitting human involvement in the decision regarding which devices areto be placed in which state.

Advantageously, in one aspect, there is provided an effective andefficient dynamic server buffering system for optimizing powerconsumption in servers while adhering to specified Service LevelAgreements (SLAs).

BRIEF DESCRIPTION OF THE DRAWINGS

The objects, features and advantages of the present invention willbecome apparent to one skilled in the art, in view of the followingdetailed description taken in combination with the attached drawings, inwhich:

FIG. 1 depicts an exemplary overview of the global manager with theactive and inactive pool managers for four inactive power states;

FIG. 2 depicts an overview of an example Resource power curve for theinactive and active states;

FIG. 3A depicts an example Transition latency matrix resource descriptor80, and FIG. 3B depicts an example transition power matrix resourcedescriptor 90;

FIG. 4 shows an example of a demand distribution plot 75 ofcluster-level demand based on an aggregation interval for workloadsdistributed over time;

FIG. 5 depicts a method of managing the inactive server pool in oneembodiment;

FIG. 6 depicts a method of managing the inactive server pool in afurther embodiment;

FIG. 7 depicts a method of managing the inactive server pool in analternate embodiment; and

FIG. 8 illustrates an exemplary hardware configuration for implementingand solving a constraint optimization problem in one embodiment.

DETAILED DESCRIPTION

In one aspect, there is provided a system, method and computer programproduct for providing automated power management techniques forcomputing systems, generally, and more particularly, the inventionrelates to an effective and efficient dynamic server buffering systemfor optimizing power consumption in servers according to specifiedconstraints. In one embodiment, power consumption optimization adheresto specified Service Level Agreements (SLAs).

Further, the system, method and computer program product providesautomated power management and addresses the tradeoff betweenresponsiveness and power savings by coordinating multiple surge responsezones in a computing cluster with different power-management statessystem characteristics. In one embodiment, the tradeoffs betweenresponsiveness and power savings are formulated as an objective functionwith constraints, and the desired number of devices in each inactivestate emerging as the solution to a constraint optimization problem.

FIG. 1 illustrates an environment, e.g., a data center, or computingcluster 10, in which the power management system and method of theinvention may be employed. As shown in FIG. 1, the system includes: anon-Demand Router 11 that receives service requests, e.g., http requests,from clients (not shown), e.g., over a communications network; a pool 15of active, powered-on computing devices 12 that provide the requiredcomputing resources for the current level of workload demand; a pool 20of inactive computing devices 13 that are unemployed under a currentresource demand level; and a Performance or Global Manager device 50which is a computing device, including a processor unit, operable forcontrolling the power settings of each of the servers 12 in the ActiveServers Pool 15 via Active Pool Manager device 35, and, the deploymentof servers from the Inactive Servers Pool 20 to the Active Servers Pool15 via Inactive Pool Manager device 45 (or, removal of servers from theActive Servers Pool 15 for placement back in the Inactive Servers Pool20).

FIG. 1 particularly shows a computing cluster 10 with multiple computingdevices 12, e.g., servers, workstations, and a distributed workload suchthat, at any given time instance: pool 15 includes active, powered-oncomputing devices 12 that provide the required computing resources forthe current level of workload demand, and pool 20 includes inactivecomputing devices 13 that are unemployed under a current resource demandlevel. The computing resources, e.g., server devices, in pool 20 are invarious states of inactivity, e.g., —at least two—distinct inactivestates, such as “idle” state 13, “standby” state 14, “hibernate” state16 and “powered-off” state 18, into which inactive devices may beplaced.

In one exemplary embodiment, the Inactive Pool Manager device 45 managesthe inactive states of all computing devices in the inactive pool. TheGlobal Manager device 50 manages the interaction of the “Active PoolManager” device 35 and “Inactive Pool Manager” device 45. For example,the global manager device 50 interfaces with the “Active Pool Manager”device 35 that executes logic configured for determining when computingdevices should be activated from the inactive pool, or returned to theinactive pool; and, further interfaces with the “Inactive Pool Manager”device 45 that executes logic configured for dividing the inactiveresources into different “inactive zones” operating at the differentinactive states and for determining the transition of inactive devicesamong the different states.

In one embodiment, the Inactive Pool Manager device 45 receives request46 from the Global Manager device 50, e.g., a request from the GlobalManager to either provide one or more computing devices from theinactive pool to the active pool, or accept one or more active computingdevices into the inactive pool. If the request was to activate computingdevices, the Inactive Pool Manager 45 selects which servers to provide,and takes steps to activate them. If the request is to accept computingdevices into the inactive pool, the Inactive Pool Manager devicede-activates one or more computing devices to an initial inactive state.Therefore, the “Inactive Pool Manager” that plans the activationtransition and the transition(s) of inactive device(s) among thedifferent inactive states (between inactive state transitions) isgenerally referred to herein as a “planner” device.

Once satisfying the Global Manager's request, the Inactive Pool Manager45 proactively manages the inactive states of each computing device asfollows: 1) by determining the desired number (and identities) ofcomputing devices to be placed in each inactive state by solving aconstraint optimization problem that describes a user-specifiedtrade-off between expected readiness (estimated time to be able toactivate computing devices when they are needed next) and conservingenergy; 2) by generating a plan for changing the current set of inactivestates to the desired set; and, by 3) executing the plan.

The abovementioned embodiment can be described more specifically interms of the following set of quantities:

a set of activation states (e.g. active, idle, standby, hibernate,shutdown-bare, . . . );

an activation vector A_(i) representing the number of servers currentlyor prospectively in each activation state i;

a transition latency matrix T_(ij), representing the expected timerequired to change the activation state of a server from i to j;

a power vector P_(i), representing the average power consumption of aserver while in activation state i;

a readiness vector R, where the k^(th) component R_(k) represents theminimal amount of time it would take for k inactive servers to berestored to an active state given a specific activation vector A and thetransition latency matrix T; and

a desired readiness vector R⁰, where the k^(th) component R⁰ ₁,represents a specified constraint on the maximum time permitted for kinactive servers to be restored to an active state.

With reference to these defined quantities, a method of managing theinactive server pool in accordance with this embodiment is depicted bythe flow chart in FIG. 5, as follows. In the method 100, it is giventhat, as depicted at step 105, the performance manager, i.e., GlobalManager device 50 initiates an activation or a deactivation request. Ifthe request is for activation, control passes to step 112, at which theperformance manager generates an activation request to the Inactive PoolManager (IPM) to activate the quantity of “k” servers. The number ofservers to be activated, k, may be chosen according to a number ofcriteria or rules, typically for the purpose of providing a desiredlevel of performance (e.g., as governed by an SLA between parties). Atstep 114, the IPM identifies the k most ready servers from theactivation vector A, i.e. those for which the corresponding transitionlatencies are the least. Then, at step 116, the servers identified atstep 114 are brought to the active state to satisfy the performancemanager. Control then passes to step 130 where the IPM computes theresulting activation vector A′. On the other hand, if at step 105, theGlobal Manager device 50 decides to initiate a deactivation request, itspecifies (at step 122) a set of k active servers that are to bedeactivated, and moved from the active pool 15 into the inactive pool20. Control then passes to step 124, at which point the k active serversidentified by the Global Pool Manager device are placed in a choseninactive state in the inactive pool. Control then passes to step 130.

Regardless of whether servers have been activated or deactivated, atstep 130 a new activation vector A′ is computed by the IPM. In oneembodiment, before computing new activation vector A′, one approach isto wait until the activation steps undertaken at step 116 or thede-activation steps undertaken at step 124 have completed, and observehow many servers are in each inactive state to derive A′. A secondapproach is to anticipate what the activation vector will be when steps116 or 124 have completed, which is computed from the originalactivation vector A and a knowledge of which servers are makingtransitions and their original and destination states.

From step 130, control then passes to step 140, at which an optimalactivation vector A″ is computed. In this preferred embodiment, aconstraint-optimization problem is formulated and solved to generate A″.One example of such a constraint-optimization problem is to select A″ soas to minimize the expected power consumption Σ_(i) A_(i) P_(i) (wherethe index i runs across all inactive servers) subject to the constraintthat R_(k)≦R⁰ _(k) for all k. The solution can be computed by any of anumber of existing constraint-optimization techniques known in the art,ranging from methods such as exhaustive search to ones such as areembodied in the known CPLEX® (Trademark of CPLEX Optimization Inc.,TEXAS) optimization software package.

Next, as shown in FIG. 5, control passes to step 150, at which the IPMgenerates a plan consisting of a sequence of actions required to movethe system from activation A′ to activation A″. In one embodiment, theseactions are performed in parallel. These actions include transitioningservers from one inactive state to another to reach the desired powerstate for each server. In one example implementation, the methodcomprises computing a generated plan as that which minimizes the timerequired to accomplish the switch from A′ to A″, as may be computedusing the transition latency matrix T.

Finally, control passes to Step 160, at which the transition plangenerated at step 150 is executed, bringing the system to activationstate A″.

As an explicit example in accordance with the first embodiment, a device12, e.g., a server, in the cluster may be in one of the followingactivation states with respect to a given application or set ofapplications that are intended to run on that server: 0) active mode, inwhich it is fully on and operational and processing workload; 1) idlemode, in which the server is idle but ready to accept workload nearlyinstantaneously; 2) standby mode, in which the server architecturalstate is saved in memory and the processors and part of the system areput into low-power state; 3) hibernate mode, in which the serverarchitectural and memory state are saved into disk, and variouscomponents of the server such as the memory and CPU are in low powerconsumption mode; and, 4) shutdown-prepared mode, in which allcomponents are completely powered down but the operating system,middleware and software needed by the application are loaded on theserver. Servers may even be in any of several less-prepared states ofreadiness with respect to the application(s) of interest. For example,the server may be in a 5) shutdown-bare mode, in which it is necessaryto install some combination of the operating system, hypervisor,middleware, and/or software on the server (either by installing them viatraditional methods or by loading a virtual machine image) before it isable to run the application of interest, or a 6) shutdown-teardown mode,in which the server needs to have its current software, middleware andoperating system removed before it is ready to be re-provisioned withthe appropriate operating system, software and middleware.

Given the aforementioned definition of the server activation states, inan illustrative example, supposing that there are 2 active servers and 6inactive servers (1 in idle mode, 1 in standby mode, 1 in hibernatemode, 1 in shutdown-prepared mode, and 2 in shutdown-bare mode), theactivation vector A would be represented as:

A₀=2

A₁=1

A₂=1

A₃=1

A₄=1

A₅=2

A₆=0

Or, more compactly, A=(2,1,1,1,1,2,0).

Continuing this example, consider a transition latency matrix 80 asgiven in FIG. 3A. The average transition latency T_(ij) associated witheach pair of readiness states i and j may be known a priori, or may beestablished with a calibration process to be described herein below ingreater detail. In the example transition latency matrix 80 of FIG. 3A,the transition to the active state takes 10⁻³ seconds from the idlestate, 12 seconds from standby, 120 seconds from hibernate, 400 secondsfrom shutdown-prepared, 600 seconds from shutdown-bare, and 720 secondsfrom shutdown-teardown.

Furthermore, for this example, suppose that the expected average powerconsumption in the various states is

P₆=5 watts

P₅=5 watts

P₄=5 watts

P₃=10 watts

P₂=20 watts

P₁=50 watts

P₀=150 watts

Or, more compactly, P=(150,50,20,10,5,5,5).

Continuing the example further, a user may specify a desired state ofreadiness via the desired readiness vector R⁰. For example, anadministrator or an automated entity such as a workload managerdetermines that, given the historical volatility of a given workload, itis advisable for it to take no more than 5 seconds for a single inactiveserver to be brought to the active state, no more than 30 seconds fortwo servers to be brought to the active state, and no more than 180seconds for three servers, no more than 400 seconds for four servers, nomore than 600 seconds for five servers, and no restrictions on how longit can take for 6 or more servers to be brought back to the active statein the event of a sudden surge in workload. Then the administrator orworkload management software uses an interface to set the desiredreadiness vector to the values R⁰=(5, 30, 180, 400, 600), with R⁰k setto infinity for k>5.

In this embodiment, the constraint optimization problem is to computethe activation vector A such that:

the actual readiness vector R will not exceed R⁰ in any component, i.e.R_(k)≦R⁰ _(k) for all k; and

the expected aggregate power consumption for activation vector A, Σ_(i)A_(i) P_(i) is minimized (the summation index range need not include theactive state i=0, although whether or not it does is immaterial becausethe active state manager will already have determined A₀, so allpossible solutions will share the same value for it.).

Note that the k^(th) component of the actual readiness vector R of anygiven activation vector A can be computed as the expected time for kinactive servers to be placed in the active state, provided that themost efficient route to activation is taken in terms of servertransition latencies. Thus R_(k) is computable from the activationvector A, the transition latency matrix T, and certain knowledge aboutwhether servers can be activated serially or in parallel. For example,suppose the A is given as above: A=(2,1,1,1,1,2,0), T is given as inFIG. 3A, and servers may be activated in parallel. Then R₁=10⁻³ secondsbecause that is the time required to place the server in standby mode inactive mode. R₂=12 seconds, because creating two active servers requiresthat the first server be activated from idle mode, which takes 10⁻³seconds, and the second server must be activated from standby mode,which takes 12 seconds. If the two servers can be activated in parallel,the total time required to make two servers active is 12 seconds.Similarly, one can compute R₃=120 seconds, R₄=400 seconds, and R₅=R₆=600seconds if it is assumed that the two servers in shutdown-bare modecould be activated in parallel in one embodiment. For k>6, R_(k) isinfinite because there are no additional servers available in theinactive pool to satisfy a higher k. Thus, for the activation vectorA=(2,1,1,1,1,2,0), R=(10-3, 12, 120, 400, 600, 600), with R_(k) infinitefor k>6. Comparing the computed readiness R vector with the desiredreadiness vector R⁰=(5, 30, 180, 400, 600), it is found that theconstraint R_(k)≦R⁰ _(k) is satisfied for all k. Thus this activationvector would satisfy the constraint. The corresponding total powerconsumption of the inactive pool is 50+20+10+5+2*5+0*5=95 watts in thisexample.

In order to determine the optimal activation vector among all for whichthe number of inactive servers is equal to the current number ofinactive servers, an exhaustive search is conducted over all possibleactivation vectors to find the one that minimizes the total powerconsumption of the inactive pool while satisfying the readiness vectorconstraint, or use any of a number of more sophisticated constraintoptimization methods such as are embodied in the known CPLEXoptimization software package. In this example, it turns out thatA=(2,1,1,1,1,2,0) is the optimal activation vector.

In alternate embodiments, the method is substantially similar to thefirst embodiment, except that the desired readiness is described in amanner other than as a specified constraint on the maximum timepermitted for k inactive servers to be restored to an active state. Animportant class of such alternate embodiments is one for which the firstembodiment is preceded with a step in which the alternate way ofexpressing desired readiness is translated into the aforementioneddesired readiness vector R⁰. For example, in a second embodiment, inlieu of the readiness vector R⁰, a desired demand fluctuation responsevector F⁰ is provided, such that the k^(th) component F⁰ _(k) representsthe maximum time permitted for a plurality of servers to be allocated soas to provide acceptable performance should the workload intensityincrease by a fraction g_(k)≦g≦g_(k+1) above its present level. Theworkload intensity may be expressed in terms of number of clients,number of requests per second, or any other suitable metric. Thefractions g_(k) may be set to any values, but are preferentially setsuch that the lowest value g₀ is set to zero and the highest value isset to infinity so that the full range of possible rises in demand canbe covered. An example is provided in the table below, which canequivalently be expressed as F⁰=(0, 15, 120, 400, 600, 720, ∞) and g=(0,0.1, 0.2, 0.3, 0.5, 0.8, ∞). As summarized in TABLE 1 below, theinterpretation is that a workload increase of up to 10% above thepresent level must be handled immediately without violating acceptablelimits on performance; a workload increase of 10-20% above the presentlevel must be handled acceptably within 15 seconds, a workload increaseof 20-30% must be handled acceptably within 120 seconds, and so on, upto the final requirement that a workload increase of 80% or more behandled within 720 seconds.

TABLE 1 k Demand Rise Fraction g_(k) F⁰ _(k) (sec) 0 0% 0 1 10% 15 2 20%120 3 30% 400 4 50% 600 5 80% 720 6 ∞ ∞

This second embodiment is identical to the first embodiment, except thatin the second embodiment the method of the first embodiment is precededby a first step of converting from the requirement expressed in terms ofreadiness F⁰ to one expressed in terms of the readiness vector R⁰. Allsubsequent steps are completely the same as in the first embodiment.Specifically, for each value k, an algorithm computes the minimal numberof servers required to achieve an acceptable performance given theassumption that the demand is increased by a fraction g_(k) above itspresent value. What constitutes acceptable performance depends on thenature of the application and the preferences of the administrator. Oneform of preference is to establish an upper limit on the CPU utilizationpermitted on a server, or among a set of servers; e.g., 80% or 90% maybe used as values for this threshold. An alternative is to expresspreferences directly in terms of application metrics such as responsetime: for example, the administrator might specify that the responsetime for a given web application should not exceed two seconds for morethan 5% of the requests. The algorithm that computes the minimal numberof servers required to achieve the specified acceptable performance fora given assumed demand may, for example, comprise a queuing-theoreticalgorithm coupled with an optimization algorithm. In one embodiment ofthe algorithm, a hypothetical workload intensity λ_(k) is generated foreach value of k by multiplying the current workload by (1+g_(k)), whereg_(k) is the fraction of increase in workload intensity (e.g., see Table1). The type of arrival process (e.g. Markov, Deterministic, or General)is either assumed, or estimated from measured arrival statistics. Theservice process type is likewise assumed or estimated from statistics.For each hypothetical workload intensity, a series of one or morehypothetical number of servers is assumed. A standard queuing theoryformula or a numerical procedure (e.g. based on formulas and proceduresfrom the queuing theory textbooks Queuing Systems, Volume I and QueuingSystems, Volume II by Leonard Kleinrock) is used to compute theestimated performance (i.e. an estimated response-time distribution,throughput, and/or average server utilization, depending on which is theperformance metric of interest). An optimization algorithm (e.g.exhaustive search or binary search) examines the estimated performancemeasures produced by the queuing algorithm, and identifies for eachassumed workload intensity λ_(k) the minimal number of servers s*_(k)for which the computed performance lies within a range deemed acceptableby the administrator.

For example, suppose there is a supply of identical-capacity servers,and that the current workload can be satisfied with acceptableperformance by 10 servers. Further consider that 10% additional workloadcan be accommodated with acceptable performance by one additionalserver, 20% additional workload can be accommodated by two additionalservers, 30% additional workload can be accommodated by three additionalservers, 50% additional workload can be accommodated by five additionalservers, and 80% additional workload can be accommodated by eightadditional servers. Then several components of the equivalent desiredreadiness vector R⁰ are automatically identified from these results:namely, R⁰ ₁=F⁰ ₁, R⁰ ₂=F⁰ ₂, R⁰ ₃=F⁰ ₃, R⁰ ₅=F⁰ ₄, and R⁰ ₈=F⁰ ₅. Toobtain the readiness for 4 servers, R⁰ ₄, one may make the pessimisticassumption that it is equal to that for 5 servers since it is nototherwise specified; hence R⁰ ₄=F⁰ ₄. Similarly, the pessimisticassumption leads to R⁰ ₆=F⁰ ₅ and R⁰ ₇=F⁰ ₅. For a plurality of serversgreater than 8, the fact that no readiness value exceeds 720 seconds maybe used to infer that R⁰ _(k)=F⁰ ₅ for k>5. Thus R⁰=(0, 15, 120, 400,600, 600, 720, 720, 720) and R⁰ _(k)=720 for k>8. Now, having derivedthe desired readiness vector, the remaining steps are exactly asdescribed in the first embodiment.

In further alternate embodiments of the invention, the user can specifyalternative measures of preferences in place of the aforementionedreadiness vector R⁰. For example, in a third embodiment, the steps arenearly the same as in the first embodiment represented in FIG. 5, exceptthat the specified system goal (i.e., request) is different: it is tomaintain the expected time to supply any additional servers required bythe Global Pool manager below a specified upper threshold T_(max). Thesteps of this third embodiment are depicted in FIG. 6. In this thirdembodiment, steps 205, 212, 214, 216, 222, 224 and 230 are exactly thesame as their counterparts 105, 112, 114, 116, 122, 124 and 130 in FIG.5. The differences from the first embodiment are as follows: First, atstep 207 in FIG. 6, there is specified a value T_(max), representing amaximum expected time to activate additional servers. Also, at step 209,a predictive algorithm computes probabilities pi for i additionalservers to be needed the next time any additional servers are needed,where i runs from 1 to a specified upper threshold beyond which theprobabilities are assumed to be zero. The predictive algorithm can bebased on statistical or pattern-based predictors, or can employ othertimeseries forecasting techniques such as linear regression,autoregressive moving average and neural networks (e.g., see EvelynDuesterwald, Calin Cascaval, Sandhya Dwarkadas, “Characterizing andPredicting Program Behavior and its Variability, Proceedings of the 12thInternational Conference on Parallel Architectures and CompilationTechniques,” p. 220, Sep. 27-Oct. 1, 2003; and, S. M. Kendall and J. K.Ord. Time Series. Oxford University Press, New York, third edition,1990.] Step 240 is similar in nature to Step 140 in FIG. 5, except thatthe constraint optimization problem from which the desired activationvector A″ is computed is different. At Step 240, A″ is computed as theactivation vector which minimizes the expected power consumption Σ_(i)A″_(i) P_(i) given the constraint Σ_(i) R_(i) p_(i)<T_(max), where, asbefore, the readiness R is computed from the activation vector A. Theweighted sum Σ_(i)R_(i)p_(i) represents the expected time required tomake the required number of servers available. Once the desiredactivation vector is computed at Step 240, all subsequent steps areidentical to those of the first embodiment, i.e. Steps 250 and 260 areidentical to Steps 150 and 160 of FIG. 5.

In a preferred embodiment, the probabilities p_(s) for “s” servers to berequired for acceptable performance are computed as follows: Supposec(w), the cumulative workload intensity distribution as a function ofworkload intensity “w”, is known. Such a function c(w) is depicted forexample in FIG. 4 which shows an example of a demand distribution plot75 of cluster-level demand based on an aggregation interval forworkloads distributed over time. For each integer value of the number ofservers “s”, an algorithm computes a maximal workload w(s) 77 for which“s” servers can attain a performance level that is deemed acceptable.The vertical bar, 77, in FIG. 4 shows an example to this attainableworkload intensity level w(s), for the number of servers equal to “s”.The corresponding cumulative distribution value, c(w(s)) denotes theprobability that the observed cluster-level workload will be less thanor equal to w(s). The algorithm for computing w(s) may be similar tothat described herein above, which included computing the inversefunction s(w). Specifically, the algorithm may comprise aqueuing-theoretic algorithm that computes performance metrics as afunction of an assumed workload and server capacity, coupled with anoptimization algorithm (e.g., exhaustive search) that repeatedly runsthe queuing-theoretic algorithm for multiple assumptions about thenumber workload to determine the maximal workload “w” that could behandled for a given number of servers “s” such that a given performancecriterion is met. The probability p_(s) for “s” servers to be requiredmay be computed as p_(s)=c(w(s))−c(w(s−1)). This probability is shown inFIG. 4, as the difference between the two cumulative density valuesc(w(s)) and c(w(s−1)) corresponding to the attainable workload intensityfor s servers, shown as w(s) as indicated at vertical bar 77, and theattainable workload intensity for “s−1” servers, shown as w(s−1) asindicated at vertical bar 72, respectively.

In a fourth embodiment, the computation of the desired activation vectorA″ takes into consideration a further constraint, objective or tradeoffbased on minimizing wear-and-tear on computing resources that can resultfrom changing their activation state. For example, the nature of theconstraint or objective could be such as to discourage or forbid theabsolute total number of changes in activation state from exceeding aspecified value. Alternatively, the constraint or objective could beconstructed to discourage or forbid the number of changes in activationstate within any given time period from exceeding a given upper limit.Alternatively, the constraint or objective might be based on thespecific activation states and transitions among them, rather than justthe total number or frequency of changes.

In a fifth embodiment, shown in the flow chart of a method 300 in FIG.7, wherein steps 305, 312, 314, 316, 322, 324 and 330 are exactly thesame as their counterparts 105, 112, 114, 116, 122, 124 and 130 in FIG.5. The differences from the first embodiment are as follows: the step340 of computing a desired activation vector A″ is followed by a step342 in which a recommendation mode is employed. Here, the desiredactivation vector A″ is presented to a human operator via a graphicaluser interface at 342, that permits the human operator to modify thedesired activation vector into a user-preferred Activation Vector A′″,e.g., as shown at 344. Then the new desired activation vector is inputto the planner device at 350, a plan (sequence of actions) for movingthe system to the new desired activation vector is generated, and thenthe plan is performed at 360.

Any of the above embodiments of the invention can be extended to includea Calibration Process that automatically establishes various quantitiesrequired for computing the optimal activation vector, such as thetransition latency matrix and the power curves. The Calibration Processis triggered at the admission of a new computing resource to either ofthe pools. The calibration process works as follows: 1) A calibrationutilization benchmark—similar in operational principle to SPECpower_ssj™(trademark of the Standard Performance Evaluation Corporation:http://www.spec.org/power_ssj2008) incorporated by reference herein,that evaluates the power and performance characteristics of volumeserver class and multi-node class computers—is run at varying deviceutilizations and corresponding power utilization is monitored; idledevice power is recorded; and, for available device power states: a) thedevice is cycled through each state; and, b) Transition latencies andpower overhead, and power consumption at different states are recorded;and, based on the observed data, a “resource descriptor” is generated.

The end results of the calibration process are the generation of“resource descriptors” that include: (i) a transition latency matrix;(ii) a transition power matrix; and (iii) the resource power curve foreach computing device. FIGS. 3A and 3B, in one embodiment, and bynon-limiting example, show the example first two components of theresource descriptors computed as part of the calibration process. Forexample, the resource descriptors include data forming a Transitionlatency matrix 80 (shown in FIG. 3A) and, data forming a Transitionpower matrix 90 (shown in FIG. 3B) for a particular computing devicebeing added to a pool. In one embodiment, the Transition latency matrix80 shows latency times (e.g., in seconds) endured for rendering thedevice from a first particular state, e.g., an initial state 81, to asecond particular state, e.g., a final state 83. Further, in oneembodiment, the transition power matrix 90 shows power overhead consumed(e.g., in Watts) for rendering the device from a first particular powerstate, e.g., an initial state 91, to a second particular state, e.g., afinal state 93. The energy overhead of each state transition is deriveddirectly by multiplying the transition power and latency matrices. FIG.2, in one embodiment, and by non-limiting example, shows the power curvecomponent for one example computing device (e.g., server) being added tothe pool. In FIG. 2, the example shows a resource power curve 60 for theinactive states 65 and active states 66.

The calibration process may be triggered at the admission of a newcomputing device to a pool. The full calibration process can beperformed “eagerly” i.e., immediately after the device is added to thepool; or “lazily”, based on performance requirements, available powerbudgets and energy costs. For example, the added resources might beimmediately needed to satisfy current demand, or the time-varying energycosts and system load might make deferring calibration to a low-demand,low-cost time period preferable.

Data structures representing the resource descriptors are input into thepool managers to be used in host ordering for power-efficienttransitioning among active and inactive states. Additional provision ismade for allowing manual input in the decision regarding which devicesare to be placed in which state.

As a result, the system, method and computer program product providesdynamic buffering in which servers are maintained in various states ofreadiness, and caused to make transitions among these states ofreadiness without consuming excessive amounts of energy. In oneembodiment, transitions among these states of readiness are determinedin such a way as to maintain good SLA behavior.

FIG. 8 illustrates an exemplary hardware configuration of a computingsystem 400 running and/or implementing the method steps describedherein. The hardware configuration preferably has at least one processoror central processing unit (CPU) 411. The CPUs 411 are interconnectedvia a system bus 412 to a random access memory (RAM) 414, read-onlymemory (ROM) 416, input/output (I/O) adapter 418 (for connectingperipheral devices such as disk units 421 and tape drives 440 to the bus412), user interface adapter 422 (for connecting a keyboard 424, mouse426, speaker 428, microphone 432, and/or other user interface device tothe bus 412), a communication adapter 434 for connecting the system 400to a data processing network, the Internet, an Intranet, a local areanetwork (LAN), etc., and a display adapter 436 for connecting the bus412 to a display device 438 and/or printer 439 (e.g., a digital printerof the like).

As will be appreciated by one skilled in the art, aspects of the presentinvention may be embodied as a system, method or computer programproduct. Accordingly, aspects of the present invention may take the formof an entirely hardware embodiment, an entirely software embodiment(including firmware, resident software, micro-code, etc.) or anembodiment combining software and hardware aspects that may allgenerally be referred to herein as a “circuit,” “module” or “system.”Furthermore, aspects of the present invention may take the form of acomputer program product embodied in one or more computer readablemedium(s) having computer readable program code embodied thereon.

Any combination of one or more computer readable medium(s) may beutilized. The computer readable medium may be a computer readable signalmedium or a computer readable storage medium. A computer readablestorage medium may be, for example, but not limited to, an electronic,magnetic, optical, electromagnetic, infrared, or semiconductor system,apparatus, or device, or any suitable combination of the foregoing. Morespecific examples (a non-exhaustive list) of the computer readablestorage medium would include the following: an electrical connectionhaving one or more wires, a portable computer diskette, a hard disk, arandom access memory (RAM), a read-only memory (ROM), an erasableprogrammable read-only memory (EPROM or Flash memory), an optical fiber,a portable compact disc read-only memory (CD-ROM), an optical storagedevice, a magnetic storage device, or any suitable combination of theforegoing. In the context of this document, a computer readable storagemedium may be any tangible medium that can contain, or store a programfor use by or in connection with a system, apparatus, or device runningan instruction.

A computer readable signal medium may include a propagated data signalwith computer readable program code embodied therein, for example, inbaseband or as part of a carrier wave. Such a propagated signal may takeany of a variety of forms, including, but not limited to,electro-magnetic, optical, or any suitable combination thereof. Acomputer readable signal medium may be any computer readable medium thatis not a computer readable storage medium and that can communicate,propagate, or transport a program for use by or in connection with asystem, apparatus, or device running an instruction. Program codeembodied on a computer readable medium may be transmitted using anyappropriate medium, including but not limited to wireless, wireline,optical fiber cable, RF, etc., or any suitable combination of theforegoing.

Computer program code for carrying out operations for aspects of thepresent invention may be written in any combination of one or moreprogramming languages, including an object oriented programming languagesuch as Java, Smalltalk, C++ or the like and conventional proceduralprogramming languages, such as the “C” programming language or similarprogramming languages. The program code may run entirely on the user'scomputer, partly on the user's computer, as a stand-alone softwarepackage, partly on the user's computer and partly on a remote computeror entirely on the remote computer or server. In the latter scenario,the remote computer may be connected to the user's computer through anytype of network, including a local area network (LAN) or a wide areanetwork (WAN), or the connection may be made to an external computer(for example, through the Internet using an Internet Service Provider).

Aspects of the present invention are described below with reference toflowchart illustrations and/or block diagrams of methods, apparatus(systems) and computer program products according to embodiments of theinvention. It will be understood that each block of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer program instructions. These computer program instructions maybe provided to a processor of a general purpose computer, specialpurpose computer, or other programmable data processing apparatus toproduce a machine, such that the instructions, which run via theprocessor of the computer or other programmable data processingapparatus, create means for implementing the functions/acts specified inthe flowchart and/or block diagram block or blocks. These computerprogram instructions may also be stored in a computer readable mediumthat can direct a computer, other programmable data processingapparatus, or other devices to function in a particular manner, suchthat the instructions stored in the computer readable medium produce anarticle of manufacture including instructions which implement thefunction/act specified in the flowchart and/or block diagram block orblocks.

The computer program instructions may also be loaded onto a computer,other programmable data processing apparatus, or other devices to causea series of operational steps to be performed on the computer, otherprogrammable apparatus or other devices to produce a computerimplemented process such that the instructions which run on the computeror other programmable apparatus provide processes for implementing thefunctions/acts specified in the flowchart and/or block diagram block orblocks.

The flowchart and block diagrams in the Figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods and computer program products according to variousembodiments of the present invention. In this regard, each block in theflowchart or block diagrams may represent a module, segment, or portionof code, which comprises one or more operable instructions forimplementing the specified logical function(s). It should also be notedthat, in some alternative implementations, the functions noted in theblock may occur out of the order noted in the figures. For example, twoblocks shown in succession may, in fact, be run substantiallyconcurrently, or the blocks may sometimes be run in the reverse order,depending upon the functionality involved. It will also be noted thateach block of the block diagrams and/or flowchart illustration, andcombinations of blocks in the block diagrams and/or flowchartillustration, can be implemented by special purpose hardware-basedsystems that perform the specified functions or acts, or combinations ofspecial purpose hardware and computer instructions.

Having thus described our invention, what we claim as new, and desire tosecure by Letters Patent is:
 1. A system for managing inactive states ofcomputing devices comprising: a memory, a processor unit incommunication with said memory, for performing a method comprising:receiving, at said processor unit, a request to one of: activate ordeactivate one or more computing devices from a respective group ofinactive or active computing devices, each said inactive or activecomputing device initially in a pre-determined state of readiness;activating or deactivating said one or more computing devices, saidactivating or deactivating resulting in a number of computing devices inone or more activation states of readiness i; computing an optimalconfiguration of said computing devices in said one or more said statesof readiness i by minimizing an expected power consumption Σ_(i) A_(i)P_(i) where i represents all inactive computing device states, A_(i)represents a number of said computing devices currently in each state i,and, P_(i) represents an average power consumption of computing deviceswhile in said state i; and placing said computing devices in saidoptimized configuration, said processor unit is further configured to:formulate an objective function to be minimized, said objective functionrepresenting said expected power consumption Σ_(i) A_(i) P_(i) subjectto a constraint, wherein, after one of said activating or deactivatingone or more computing devices, said processor unit is further configuredto: compute activation vector A″ representing a number of computingdevices in said optimized one or more activation states of readiness i;specify an upper threshold T_(max) representing a maximum expected timeto activate additional computing devices; and compute probabilitiesp_(i) for i additional computing devices to be needed, where i rangesfrom 1 to a specified upper threshold, wherein said activation vector A″is computed by formulating said objective function to minimize anexpected power consumption Σ_(i) A″_(i) P_(i) given a constraintΣ_(i)R_(i)p_(i)<T_(max), where Σ_(i)R_(i)p_(i) is a weighted sumrepresenting the expected time required to make the i computing devicesavailable.
 2. The system as claimed in claim 1, wherein, after one ofsaid activating or deactivating one or more computing devices, saidprocessor unit is further configured to: compute a resulting activationvector A′ representing said resulting number of computing devices in oneor more activation states of readiness i.
 3. The system as claimed inclaim 2, wherein said processor unit is further configured to: initiatetransition of said computing devices from one inactive state to anotherto reach a desired power state for each computing device, said processorunit generating a plan to minimize a time required to accomplish saidtransitioning from said activation vector A′ to optimized activationvector A″ according to a transition latency matrix T_(ij), representingan expected time required to change an activation state of a computingdevice from activation state i to activation state j.
 4. The system asclaimed in claim 2, wherein said objective function is subject to aconstraint that R_(k)≦R⁰ _(k) for each computing devices k, wherein saidR represents a readiness vector, a k^(th) component R_(k) representing aminimal amount of time for k computing devices to be restored to anactive state given a specific activation vector A and said transitionlatency matrix T; and, R⁰ represents a specified readiness vector, ak^(th) component R⁰ _(k) representing a specified constraint on amaximum time permitted for k inactive servers to be restored to saidactive state.
 5. The system as claimed in claim 2, wherein saidprocessor unit is further configured to: specify a desired demandfluctuation response vector F⁰ such that a k^(th) component F⁰ _(k)represents a maximum time permitted for a plurality of computing devicesto be transitioned in anticipation of a workload intensity increaseabove a current level; and convert a requirement expressed in terms ofsaid fluctuation response vector F⁰ to said readiness vector R⁰.
 6. Thesystem as claimed in claim 2, further comprising: computing saidprobabilities p_(s) for “s” computing devices by: specifying a c(w) thatrepresents a cumulative workload intensity distribution as a function ofa workload intensity “w”; computing a maximal workload intensity levelw(s) for which “s” servers can attain a pre-determined performance levelw(s); computing a corresponding cumulative distribution value c(w(s)) todenote a probability that an observed cluster-level workload will beless than or equal to w(s); and computing probability p_(s) for “s”servers to be required according to:p _(s) =c(w(s))−c(w(s−1)) where cumulative density values c(w(s)) andc(w(s−1)) correspond respectively to attainable workload intensity foran amount s servers w(s) and the attainable workload intensity for anamount s−1 servers.
 7. The system as claimed in claim 2, wherein, aftercalculating said desired activation vector A″, said processor unit isfurther configured to: modify the desired activation vector into auser-preferred Activation Vector A′″; and input, to a planner device, asequence of actions for transitioning the computing devices according tosaid user-preferred Activation Vector A′″.
 8. The system as claimed inclaim 2, wherein said processor unit is further configured to: receive,at said processor unit, a request to de-activate one or more activecomputing devices; and placing said de-activated computing devices at aspecified state of readiness, thereby, resulting in a new activationvector A′; solve a constraint optimization problem for computing a bestactivation vector A″ from said activation state vector A′; generate aplan that minimizes a sequence of actions required to switch state ofsaid computing devices from activation state A′ to activation state A″;and execute the plan to bring said computing devices to said activationstate A″.
 9. A computer program product for managing inactive states ofcomputing devices, the computer program product comprising: a storagemedium readable by a processing circuit and storing instructions forexecution by the processing circuit for performing a method comprising:receiving a request to one of: activate or deactivate one or morecomputing devices from a respective group of inactive or activecomputing devices, each said inactive or active computing deviceinitially in a pre-determined state of readiness; activating ordeactivating said one or more computing devices, said activating ordeactivating resulting in a number of computing devices in one or morestates of readiness i; computing an optimal configuration of saidcomputing devices in said one or more said states of readiness i byminimizing an expected power consumption Σ_(i) A_(i) P_(i) where irepresents all inactive computing devices, A_(i) represents a number ofsaid computing devices currently in each state i, and, P_(i) representsan average power consumption of computing devices while in said state i;and placing said computing devices in said optimized configuration, andformulating an objective function to be minimized, said objectivefunction representing said expected power consumption Σ_(i) A_(i) P_(i)subject to a constraint, said optimizing including computing activationvector A″ representing a number of computing devices in said optimizedone or more activation states of readiness i. specifying an upperthreshold T_(max) representing a maximum expected time to activateadditional computing devices; and computing probabilities p_(i) for iadditional computing devices to be needed, where i ranges from 1 to aspecified upper threshold, wherein said activation vector A″ is computedby formulating said objective function to minimize an expected powerconsumption Σ_(i) A″_(i) P_(i) given a constraintΣ_(i)R_(i)p_(i)<T_(max), where Σ_(i)R_(i)p_(i) is a weighted sumrepresenting the expected time required to make the i computing devicesavailable
 10. The computer program product as claimed in claim 9,wherein, after one of said activating or deactivating one or morecomputing devices: computing a resulting activation vector A′representing said resulting number of computing devices in one or moreactivation states of readiness i.
 11. The computer program product asclaimed in claim 10, wherein said placing said computing devices in saidoptimized configuration comprises: transitioning said computing devicesfrom one inactive state to another to reach a desired power state foreach computing device, said transitioning comprising: generating a planto minimize a time required to accomplish said transitioning from saidactivation vector A′ to optimized activation vector A″ according to atransition latency matrix T_(ij), representing an expected time requiredto change an activation state of a computing device from activationstate i to activation state j.
 12. The computer program product asclaimed in claim 10, wherein said objective function is subject to aconstraint that R_(k)≦R⁰ _(k) for each computing devices k, wherein saidR represents a readiness vector, a k^(th) component R_(k) representing aminimal amount of time for k computing devices to be restored to anactive state given a specific activation vector A and said transitionlatency matrix T; and, R⁰ represents a specified readiness vector, ak^(th) component R⁰ _(k) representing a specified constraint on amaximum time permitted for k inactive servers to be restored to saidactive state.
 13. The computer program product as claimed in claim 10,further comprising: specifying a desired demand fluctuation responsevector F⁰ such that a k^(th) component F⁰ _(k) represents a maximum timepermitted for a plurality of computing devices to be transitioned inanticipation of a workload intensity increase above a current level; andconverting a requirement expressed in terms of said fluctuation responsevector F0 to said readiness vector R⁰.
 14. The computer program productas claimed in claim 10, further comprising: computing said probabilitiesp_(s) for “s” computing devices by: specifying c(w) that represents acumulative workload intensity distribution as a function of a workloadintensity “w”; computing a maximal workload intensity level w(s) forwhich “s” servers can attain a pre-determined performance level w(s);computing a corresponding cumulative distribution value c(w(s)) todenote a probability that an observed cluster-level workload will beless than or equal to w(s); and computing probability p_(s) for “s”servers to be required according to:p _(s) =c(w(s))−c(w(s−1)) where cumulative density values c(w(s)) andc(w(s−1)) correspond respectively to attainable workload intensity foran amount s servers w(s) and the attainable workload intensity for anamount s−1 servers.
 15. The computer program product as claimed in claim10, wherein, after calculating said desired activation vector A″,modifying the desired activation vector into a user-preferred ActivationVector A′″; and inputting, to a planner device, a sequence of actionsfor transitioning the computing devices according to said user-preferredActivation Vector A′″.
 16. A method for managing power consumption in asystem including computing devices in both active and one or moreinactive states of readiness, the method comprising: receiving, at aprocessing unit, a request to one of: activate or deactivate one or morecomputing devices from a respective group of inactive or activecomputing devices, each said inactive or active computing deviceinitially in a pre-determined state of readiness; activating ordeactivating said one or more computing devices, said activating ordeactivating resulting in a number of computing devices in one or morestates of readiness i; computing an optimal configuration of saidcomputing devices in said one or more said states of readiness i byminimizing an expected power consumption Σ_(i) A_(i) P_(i) where irepresents all inactive computing device states, A_(i) represents anumber of said computing devices currently in each state i, and, P_(i)represents an average power consumption of computing devices while insaid state i; and, placing said computing devices in said optimizedconfiguration, formulating an objective function to be minimized, saidobjective function representing said expected power consumption Σ_(i)A_(i) P_(i) subject to a constraint, computing an activation vector A″representing a number of computing devices in said optimized one or moreactivation states of readiness i; specifying an upper threshold T_(max)representing a maximum expected time to activate additional computingdevices; and computing probabilities p_(i) for i additional computingdevices to be needed, where i ranges from 1 to a specified upperthreshold, wherein said activation vector A″ is computed by formulatingsaid objective function to minimize an expected power consumption Σ_(i)A″_(i) P_(i) given a constraint Σ_(i)R_(i)p_(i)<T_(max), whereΣ_(i)R_(i)p_(i) is a weighted sum representing the expected timerequired to make the i computing devices available, wherein a programusing said processor unit is configured to perform one or more of saidreceiving, activating, computing, placing, formulating and computingprobabilities.
 17. The method as claimed in claim 16, wherein, after oneof said activating or deactivating one or more computing devices:computing a resulting activation vector A′ representing said resultingnumber of computing devices in one or more activation states ofreadiness i,
 18. The method as claimed in claim 17, further comprising:wherein said placing said computing devices in said optimizedconfiguration comprises: transitioning said computing devices from oneinactive state to another to reach a desired power state for eachcomputing device, said transitioning comprising: generating a plan tominimize a time required to accomplish said transitioning from saidactivation vector A′ to optimized activation vector A″ according to atransition latency matrix T_(ij), representing an expected time requiredto change an activation state of a computing device from activationstate i to activation state j.
 19. The method as claimed in claim 17,wherein said objective function is subject to a constraint that R_(k)≦R⁰_(k) for each computing devices k, wherein said R represents a readinessvector, a k^(th) component R_(k) representing a minimal amount of timefor k computing devices to be restored to an active state given aspecific activation vector A and said transition latency matrix T; and,R⁰ represents a specified readiness vector, a k^(th) component R⁰ _(k)representing a specified constraint on a maximum time permitted for kinactive servers to be restored to said active state.
 20. The method asclaimed in claim 17, further comprising: specifying a desired demandfluctuation response vector F⁰ such that a k^(th) component F⁰ _(k)represents a maximum time permitted for a plurality of computing devicesto be transitioned in anticipation of a workload intensity increaseabove a current level; and converting a requirement expressed in termsof said fluctuation response vector F⁰ to said readiness vector R⁰. 21.The method as claimed in claim 17, further comprising: computing saidprobabilities p_(s) for “s” computing devices by: specifying c(w) thatrepresents a cumulative workload intensity distribution as a function ofa workload intensity “w”; computing a maximal workload intensity levelw(s) for which “s” servers can attain a pre-determined performance levelw(s); computing a corresponding cumulative distribution value c(w(s)) todenote a probability that an observed cluster-level workload will beless than or equal to w(s); and computing probability p_(s) for “s”servers to be required according to:p _(s) =c(w(s))−c(w(s−1)); where cumulative density values c(w(s)) andc(w(s−1)) correspond respectively to attainable workload intensity foran amount s servers w(s) and the attainable workload intensity for anamount s−1 servers.
 22. The method as claimed in claim 17, wherein saidobjective function is subject to a constraint that based on minimizingwear-and-tear on computing resources that result from changing theirrespective activation state, said constraint comprising one or more of:specifying a total number of changes in activation state from exceedinga specified value, specifying a total number of changes in activationstate within any given time period from exceeding a given upper limit.23. The method as claimed in claim 17, wherein, after calculating saiddesired activation vector A″, modifying the desired activation vectorinto a user-preferred Activation Vector A′″; and, inputting, to aplanner device, a sequence of actions for transitioning the computingdevices according to said user-preferred Activation Vector A′″.
 24. Themethod as claimed in claim 17, further comprising: receiving, at saidprocessor unit, a request to de-activate one or more active computingdevices; and placing said de-activated computing devices at a specifiedstate of readiness, thereby, resulting in a new activation vector A′;solving a constraint optimization problem for computing a bestactivation vector A″ from said activation state vector A′; generating aplan that minimizes a sequence of actions required to switch state ofsaid computing devices from activation state A′ to activation state A″;and executing the plan to bring said computing devices to saidactivation state A″.